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The Wiener Stock Price Model and the Basic Principles of Black-Scholes Theory

In: The Art of Quantitative Finance Vol.1

Author

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  • Gerhard Larcher

    (Johannes Kepler University of Linz)

Abstract

We give basic tools for the statistical analysis of financial data. Especially we introduce the basic parameters trend, volatility, and correlation for stocks. Then we motivate and derive the Wiener stock price model (geometric Brownian motion). Thereby we discuss the goals and the meaning of mathematical modeling in general. We then show that—if parameters are chosen in a suitable way—the binomial N-step-model converges to the Wiener model. As a consequence we derive the Black-Scholes formula, i.e. the formula for the fair price of derivatives over an underlying which follows a Wiener model. We extensively discuss this pricing formula for plain vanilla call and put options and for strategies built by combinations of these options. We define the “Greeks” (i.e., the derivations of the fair prices with respect to different parameters), and we discuss the Greeks for various examples in detail. Finally we explain how hedging derivatives in a Wiener model is carried out.

Suggested Citation

  • Gerhard Larcher, 2023. "The Wiener Stock Price Model and the Basic Principles of Black-Scholes Theory," Springer Texts in Business and Economics, in: The Art of Quantitative Finance Vol.1, chapter 4, pages 273-516, Springer.
    • Handle: RePEc:spr:sptchp:978-3-031-23873-4_4
    DOI: 10.1007/978-3-031-23873-4_4
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